(10 points) Show by example that a single erase operation in an AVL tree may require (n)trinode restructurings (or rotations) to restore the height-balance property. Draw a schematic of an AVL tree for which this is the case; explain your answer.

Design a pos circuit that displays the letters a through j on a seven-segment indicator. the circuit has four inputs w, x, y, and z which represent the last 4 bits of the uppercase ascii code for the letter to be displayed. thus, if wxyz = 0001 then "a" will be displayed. (any answer with 22 or fewer gates and inverters, not counting any for the inputs, is acceptable)

The most complicated four letter word

Write a function balancechemical to balance chemical reactions by solving a linear set of equations. the inputs arguments are: reagents: symbols of reagents in string row array products: symbols of products in string row array elements: elements in the reaction in string row array elcmpreag: elemental composition of reactants in two dimensional numeric array elcmpprdcts: elemental composition of prducts in two dimensional numeric array hint: the first part of the problem is setting up the set of linear equations that should be solve. the second part of the problem is to find the integers from the solution. one way to do this is to mulitiply the rational basis for the nullspace by increasing larger integers until both the left-and right-side integers exist. for example, for the reaction that involves reacting with to produce and : reagents=["ch4", "o2"]; products =["co2", "h2o"]; elements =["c","h", "o"] elcmpreag=[1,4,0;